Boring tools having movable, typically rotatable cutter chips or bits, have been previously described--see German Patent Disclosure Document No. DE-OS 25 55 979. This publication shows a boring tool in which rotatable cutter chips or bits are set into the tool end such that they include an axial angle of 0.degree., or only of a few degrees. The main cutting edge of one of the bits located close to the axis of the boring tool extends over the axis, to cut along the boring tool axis. This placement is intended to prevent the formation of a small projecting tip of the material of the workpiece which remains in the middle of the bore hole, and which must be continuously torn off by chips from the remaining boring operation. In actual practice it has been found that high axial feeds of the boring tool result in some radial deflection thereof so that the main cutter bit located adjacent the axis of the boring tool can shift from beyond the actual center point. This, then, will again leave a small tip of material of the workpiece. If the feed speed is reduced, for example to zero feed, this tip is squeezed off, since the main cutting blades, upon axial unloading, will again center themselves. In the region where this squeezing or compression and deformation of the material occurs, however, high forces are applied against the hard metal cutter bit and the cutter bit may crack or chip or nick or, in a limiting case, may fracture entirely, rendering the cutter bit in the region of the main cutting area useless for further operation.